---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- arithmetic
- carry-lookahead
---

# threshold-carry-generate

Carry generate signal for carry-lookahead adders. Outputs 1 when the bit position will definitely generate a carry, regardless of incoming carry.

## Circuit

```
    a       b
    │       │
    └───┬───┘
        │
        ▼
    ┌───────┐
    │  AND  │
    │ w:1,1 │
    │ b: -2 │
    └───────┘
        │
        ▼
       G(a,b)
```

## Function

```
generate(a, b) = a AND b
```

A carry is **generated** at position i when both inputs are 1, because 1+1=10 in binary always produces a carry.

## Truth Table

| a | b | G | Meaning |
|---|---|---|---------|
| 0 | 0 | 0 | 0+0=0, no carry |
| 0 | 1 | 0 | 0+1=1, no carry |
| 1 | 0 | 0 | 1+0=1, no carry |
| 1 | 1 | 1 | 1+1=10, generates carry |

## Mechanism

The AND gate fires when both inputs contribute, guaranteeing a carry output:

- Weighted sum = a + b
- Bias = -2 requires both inputs to be 1
- Result: outputs 1 only when a=1 AND b=1

## Carry-Lookahead Context

In a carry-lookahead adder, each bit position computes two signals:

| Signal | Function | Meaning |
|--------|----------|---------|
| **G (Generate)** | a AND b | Will produce carry regardless of Cin |
| **P (Propagate)** | a XOR b | Will pass through incoming carry |

The carry equation becomes:
```
C[i+1] = G[i] OR (P[i] AND C[i])
```

For multi-bit lookahead:
```
C[4] = G[3] OR (P[3] AND G[2]) OR (P[3] AND P[2] AND G[1]) OR (P[3] AND P[2] AND P[1] AND G[0]) OR (P[3] AND P[2] AND P[1] AND P[0] AND C[0])
```

## Parameters

| | |
|---|---|
| Weights | [1, 1] |
| Bias | -2 |
| Inputs | 2 |
| Outputs | 1 |
| Neurons | 1 |
| Layers | 1 |
| Parameters | 3 |
| Magnitude | 4 |

## Usage

```python
from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def carry_generate(a, b):
    inp = torch.tensor([float(a), float(b)])
    return int((inp @ w['and.weight'].T + w['and.bias'] >= 0).item())

# Examples
print(carry_generate(0, 0))  # 0
print(carry_generate(0, 1))  # 0
print(carry_generate(1, 0))  # 0
print(carry_generate(1, 1))  # 1 (generates carry)
```

## Applications

- Carry-lookahead adders (CLA)
- Parallel prefix adders (Kogge-Stone, Brent-Kung, etc.)
- High-speed ALU design
- Multiplier partial product reduction

## Related Circuits

- `threshold-carry-propagate`: The P signal (a XOR b)
- `threshold-carrylookahead4bit`: 4-bit CLA using G and P
- `threshold-kogge-stone`: Parallel prefix adder

## Files

```
threshold-carry-generate/
├── model.safetensors
├── model.py
├── create_safetensors.py
├── config.json
└── README.md
```

## License

MIT